On the Irrationality Measure of $\ln7$
Matematičeskie zametki, Tome 107 (2020) no. 3, pp. 366-375
Cet article a éte moissonné depuis la source Math-Net.Ru
Using an integral construction based on symmetrized polynomials, we obtain a new estimate for the irrationality measure of the number $\ln7$. This estimate improves a result due to Wu, which was proved in 2002.
Keywords:
irrationality measure, linear forms, Laplace theorem, saddle-point method.
@article{MZM_2020_107_3_a3,
author = {I. V. Bondareva and M. Yu. Luchin and V. Kh. Salikhov},
title = {On the {Irrationality} {Measure} of $\ln7$},
journal = {Matemati\v{c}eskie zametki},
pages = {366--375},
year = {2020},
volume = {107},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_2020_107_3_a3/}
}
I. V. Bondareva; M. Yu. Luchin; V. Kh. Salikhov. On the Irrationality Measure of $\ln7$. Matematičeskie zametki, Tome 107 (2020) no. 3, pp. 366-375. http://geodesic.mathdoc.fr/item/MZM_2020_107_3_a3/
[1] Q. Wu, “On the linear independence measure of logarithms of rational numbers”, Math. Comp., 72:242 (2002), 901–911 | DOI | MR
[2] M. Hata, “Rational approximations to $\pi$ and some other numbers”, Acta Arith., 63:4 (1993), 325–349 | MR
[3] V. Kh. Salikhov, “O mere irratsionalnosti $\ln3$”, Dokl. AN, 417:6 (2007), 753–755 | MR
[4] Q. Wu, L. Wang, “On the irrationality measure of $\log3$”, J. Number Theory, 142 (2014), 264–273 | DOI | MR